A fundamental description of such a device is included, for example, in the paper “Adaptive Cruise Controls—System Aspects and Development Trends,” given by Winner, Witte et al., at SAE 96, Feb. 26 to 29, 1996 in Detroit (SAE Paper No. 961010). To detect vehicles traveling ahead and stationary as well as moving objects, the majority of the known systems use a microwave radar beam or an infrared lidar beam. This beam is reflected by the objects and received by the sensor, thereby making it possible to determine the relative position and relative speed of the object. The future travel-path area of the vehicle can be predicted from this information, as is described in detail in German Patent No. DE 197 22 947 C1.